General Equilibrium Amplification and Crisis Vulnerability: Cross-Crisis Evidence from Global Banks

This paper develops a continuous framework for analyzing financial contagion that incorporates both geographic proximity and interbank network linkages. The framework characterizes stress propagation through a master equation whose solution admits a Feynman-Kac representation as expected cumulative stress along stochastic paths through spatial-network space. From this representation, I derive the General Equilibrium Amplification Factor -- a structural measure of systemic importance that captures the ratio of total system-wide effects to direct effects following a localized shock. The amplification factor decomposes naturally into spatial, network, and interaction components, revealing which transmission channels contribute most to each institution's systemic importance. The framework nests discrete cascade models as a limiting case when jump intensity becomes infinite above default thresholds, clarifying that continuous and discrete approaches describe different regimes of the same phenomenon. Empirical validation using 38 global banks across the 2008 financial crisis and COVID-19 pandemic demonstrates that the amplification factor correctly identifies systemically important institutions (Pearson correlation $\rho = -0.450$, $p = 0.080$ between amplification factor and crisis drawdowns) and predicts crisis outcomes out-of-sample ($\rho = -0.352$ for COVID-19). Robustness analysis using cumulative abnormal returns -- a measure more directly connected to the Feynman-Kac integral -- strengthens these findings ($\rho = -0.512$, $p = 0.042$). Time-series analysis confirms that average pairwise bank correlations track macroeconomic stress indicators ($\rho = 0.265$ with VIX, $p